The line \(3y + 6x\) = 48 passes through the points A(-2, k) and B(4,…

Explanation

The line: \(3y + 6x\) = 48

Divide through by 3

⇒ y + 2\(x\) = 16

⇒ y = -2\(x\) + 16

∴ The gradient of the line = -2

The points: A(-2, k) and B (4, 8)

m =\(\frac{y2 - y1}{x2 - x1} = \frac{8 - k}{4 - (-2)}\)

⇒ m =\(\frac[8 - k}{4 + 2} = {8 - k}{6}\)

Since the line passes through the points

∴ -2 = \(\frac{8 - k}{6}\)

⇒ \(\frac{-2}[1} = \frac{8 - k]{6}\)

⇒ 8 - k = -12

⇒ k = 8 + 12

∴ k = 20

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